Analysis of zz-www.sudokuoftheday.co.uk-20190424-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019
level: medium
position: .4.1...86.....6571..5.............6....8....7....31.2.8...57...6.1.....54.....9.. initial
Autosolve
position: 74.1.5.86....46571165....9........6....86..57..6.31.2.8..457612621...745457612938 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D2: 2,9 => CTR => D2: 3 * DIS # C1: 2,9 => CTR => C1: 3 * DIS # G3: 2,3 => CTR => G3: 4 * PRF # G3: 4 => SOL * DIS # C1: 9 => CTR => C1: 2,3 * DIS # G3: 2 => CTR => G3: 3,4 * DIS # A4: 5,9 => CTR => A4: 3 * PRF # A4: 3 => SOL * DIS # D4: 2,7 => CTR => D4: 5 * PRF # D4: 5 => SOL * DIS # E3: 8 => CTR => E3: 2,7 * DIS # C4: 4,9 => CTR => C4: 3,8 * DIS # C5: 2,3 => CTR => C5: 4,9 * DIS # D4: 2 => CTR => D4: 5,7 * PRF # A4: 3,9 => SOL * DIS # A4: 5 => CTR => A4: 3,9 * DIS # B4: 3,9 => CTR => B4: 1,7,8 * DIS # C4: 3,9 => CTR => C4: 4,8 * PRF # G4: 1,3 => SOL * DIS # G4: 8 => CTR => G4: 1,3 * DIS # B5: 9 => CTR => B5: 1,3 * DIS # B2: 3,9 => CTR => B2: 8 * PRF # B2: 8 => SOL * DIS # B4: 3,9 => CTR => B4: 1,7,8 * DIS # B5: 3,9 => CTR => B5: 1 * PRF # B5: 1 => SOL * DIS # C2: 3,9 => CTR => C2: 2,8 * DIS # C4: 3,9 => CTR => C4: 4,8 * DIS # C5: 3,9 => CTR => C5: 2,4 * DIS # D2: 2 => CTR => D2: 3,9 * CNT 30 HDP CHAINS / 47 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D2: 2,9 => CTR => D2: 3 * DIS D2: 3 # A4: 5,9 => CTR => A4: 3 * PRF D2: 3 + A4: 3 => SOL * STA D2: 3 + A4: 3 * CNT 3 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .4.1...86.....6571..5.............6....8....7....31.2.8...57...6.1.....54.....9.. | initial |
| 74.1.5.86....46571165....9........6....86..57..6.31.2.8..457612621...745457612938 | autosolve |
| 743195286982346571165278493378524169214869357596731824839457612621983745457612938 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (18) E1: 2,9 F3: 3,8 G1: 2,3 I3: 3,4 A6: 5,9 E4: 2,7 F4: 4,9 F5: 4,9 D6: 5,7 I4: 3,9 G5: 1,3 G6: 4,8 I6: 4,9 B7: 3,9 C7: 3,9 D8: 3,9 E8: 8,9 F8: 3,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B4,B5: 1.. / B4 = 1 => 0 pairs (X) / B5 = 1 => 0 pairs (_) G4,G5: 1.. / G4 = 1 => 0 pairs (*) / G5 = 1 => 0 pairs (X) B4,G4: 1.. / B4 = 1 => 0 pairs (X) / G4 = 1 => 0 pairs (_) B5,G5: 1.. / B5 = 1 => 0 pairs (*) / G5 = 1 => 0 pairs (X) G1,G3: 2.. / G1 = 2 => 19 pairs (_) / G3 = 2 => 0 pairs (X) A5,C5: 2.. / A5 = 2 => 19 pairs (_) / C5 = 2 => 0 pairs (X) D4,E4: 2.. / D4 = 2 => 0 pairs (X) / E4 = 2 => 16 pairs (_) A2,A5: 2.. / A2 = 2 => 0 pairs (X) / A5 = 2 => 19 pairs (_) B7,C7: 3.. / B7 = 3 => 16 pairs (_) / C7 = 3 => 0 pairs (X) D8,F8: 3.. / D8 = 3 => 0 pairs (X) / F8 = 3 => 16 pairs (_) C1,G1: 3.. / C1 = 3 => 19 pairs (_) / G1 = 3 => 0 pairs (X) F3,F8: 3.. / F3 = 3 => 0 pairs (X) / F8 = 3 => 16 pairs (_) I3,I4: 3.. / I3 = 3 => 0 pairs (*) / I4 = 3 => 0 pairs (X) G3,I3: 4.. / G3 = 4 => 0 pairs (*) / I3 = 4 => 0 pairs (X) C4,C5: 4.. / C4 = 4 => 0 pairs (X) / C5 = 4 => 18 pairs (_) F4,F5: 4.. / F4 = 4 => 18 pairs (_) / F5 = 4 => 0 pairs (X) G6,I6: 4.. / G6 = 4 => 0 pairs (X) / I6 = 4 => 0 pairs (_) C4,F4: 4.. / C4 = 4 => 0 pairs (X) / F4 = 4 => 18 pairs (_) C5,F5: 4.. / C5 = 4 => 18 pairs (_) / F5 = 4 => 0 pairs (X) G3,G6: 4.. / G3 = 4 => 0 pairs (*) / G6 = 4 => 0 pairs (X) I3,I6: 4.. / I3 = 4 => 0 pairs (X) / I6 = 4 => 0 pairs (_) A4,A6: 5.. / A4 = 5 => 0 pairs (X) / A6 = 5 => 0 pairs (_) D4,D6: 5.. / D4 = 5 => 0 pairs (*) / D6 = 5 => 0 pairs (X) A4,D4: 5.. / A4 = 5 => 0 pairs (X) / D4 = 5 => 0 pairs (_) A6,D6: 5.. / A6 = 5 => 0 pairs (*) / D6 = 5 => 0 pairs (X) D3,E3: 7.. / D3 = 7 => 0 pairs (X) / E3 = 7 => 16 pairs (_) B4,B6: 7.. / B4 = 7 => 0 pairs (*) / B6 = 7 => 0 pairs (X) B6,D6: 7.. / B6 = 7 => 0 pairs (X) / D6 = 7 => 0 pairs (_) E3,E4: 7.. / E3 = 7 => 16 pairs (_) / E4 = 7 => 0 pairs (X) B2,C2: 8.. / B2 = 8 => 0 pairs (*) / C2 = 8 => 0 pairs (X) E3,F3: 8.. / E3 = 8 => 0 pairs (X) / F3 = 8 => 16 pairs (_) G4,G6: 8.. / G4 = 8 => 0 pairs (X) / G6 = 8 => 0 pairs (_) E8,F8: 8.. / E8 = 8 => 16 pairs (_) / F8 = 8 => 0 pairs (X) B6,G6: 8.. / B6 = 8 => 0 pairs (X) / G6 = 8 => 0 pairs (_) C2,C4: 8.. / C2 = 8 => 0 pairs (X) / C4 = 8 => 0 pairs (_) E3,E8: 8.. / E3 = 8 => 0 pairs (X) / E8 = 8 => 16 pairs (_) F3,F8: 8.. / F3 = 8 => 16 pairs (_) / F8 = 8 => 0 pairs (X) E1,D2: 9.. / E1 = 9 => 16 pairs (_) / D2 = 9 => 0 pairs (X) F4,F5: 9.. / F4 = 9 => 0 pairs (X) / F5 = 9 => 18 pairs (_) I4,I6: 9.. / I4 = 9 => 0 pairs (*) / I6 = 9 => 0 pairs (X) B7,C7: 9.. / B7 = 9 => 0 pairs (X) / C7 = 9 => 16 pairs (_) D8,E8: 9.. / D8 = 9 => 16 pairs (_) / E8 = 9 => 0 pairs (X) C1,E1: 9.. / C1 = 9 => 0 pairs (X) / E1 = 9 => 16 pairs (_) D2,D8: 9.. / D2 = 9 => 0 pairs (X) / D8 = 9 => 16 pairs (_) E1,E8: 9.. / E1 = 9 => 16 pairs (_) / E8 = 9 => 0 pairs (X) * DURATION: 0:00:54.562225 START: 05:33:45.789242 END: 05:34:40.351467 2019-05-01 * CP COUNT: (45) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B7,C7,D6,D8,E1,E4,E8,F3,F4,F5,F8,G1,G5,G6,I3,I4,I6) * 74.1.5.86....46571165....9........6....86..57..6.31.2.8..457612621...745457612938 * PAIR E1: 2,9 BLK 2 D2: 2,9,3 # reduction candidate for 2,9 D2: 2,9 => CTR * 74.1.5386....46571165...294.1....863...86.1575.6.314298..457612621...745457612938 D2: 3 # 19 pairs * PAIR E1: 2,9 ROW 1 C1: 2,9,3 # reduction candidate for 2,9 C1: 2,9 => CTR * 74.1.5386....46571165...294.1....863...86.1575.6.314298..457612621...745457612938 C1: 3 # 19 pairs * PAIR G1: 2,3 BLK 3 G3: 2,3,4 # reduction candidate for 2,3 G3: 2,3 => CTR * 74.1.5.86....46571165....94.1....863...86.1575.6.314298..457612621...745457612938 G3: 4 => SOLVED * 743195286982346571165278493378524169214869357596731824839457612621983745457612938 * PAIR G1: 2,3 ROW 1 C1: 2,3,9 # reduction candidate for 2,3 C1: 9 => CTR * 749125386...946571165...294...27..63...86.157.76531.2.8..457612621...745457612938 C1: 2,3 # 16 pairs * PAIR I3: 3,4 BLK 3 G3: 3,4,2 # reduction candidate for 3,4 G3: 2 => CTR * 74.1.5386....46571165...294.1....863...86.1575.6.314298..457612621...745457612938 G3: 3,4 # 19 pairs * PAIR A6: 5,9 BLK 4 A4: 5,9,3 # reduction candidate for 5,9 A4: 5,9 => CTR * 74.1.53863...46571165...294.....4.63234869157..6.31429893457612621...745457612938 A4: 3 => SOLVED * 743195286982346571165278493378524169214869357596731824839457612621983745457612938 * PAIR E4: 2,7 BLK 5 D4: 2,7,5 # reduction candidate for 2,7 D4: 2,7 => CTR * 7431952862..346571165..84935....4.693..869.579765318248..457612621..3745457612938 D4: 5 => SOLVED * 743195286982346571165278493378524169214869357596731824839457612621983745457612938 * PAIR E4: 2,7 COL E E3: 2,7,8 # reduction candidate for 2,7 E3: 8 => CTR * 74.1.5.86....46571165783294....7..63...86.157.76531.2.8..457612621...745457612938 E3: 2,7 # 16 pairs * PAIR F4: 4,9 ROW 4 C4: 4,9,3,8 # reduction candidate for 4,9 C4: 4,9 => CTR * 74.1.5.86..8.46571165....9.......163...86..57..6.31.2.8..457612621...745457612938 C4: 3,8 # 19 pairs * PAIR F5: 4,9 ROW 5 C5: 4,9,2,3 # reduction candidate for 4,9 C5: 2,3 => CTR * 74.1.5.86....46571165....9...4..9.63...864157..6.31.298..457612621...745457612938 C5: 4,9 # 21 pairs * PAIR D6: 5,7 BLK 5 D4: 5,7,2 # reduction candidate for 5,7 D4: 2 => CTR * 7431952862..3465711657284935..274.693..869.579765318248..457612621..3745457612938 D4: 5,7 # 16 pairs * PAIR I4: 3,9 ROW 4 A4: 3,9,5 # reduction candidate for 3,9 A4: 3,9 => SOLVED * 743195286982346571165278493378524169214869357596731824839457612621983745457612938 A4: 5 => CTR * 7431952862..346571165..84935....4.693..869.579765318248..457612621..3745457612938 B4: 3,9,1,7,8 # reduction candidate for 3,9 B4: 3,9 => CTR * 743195286.8.346571165..8493......16..1.86.357.765318248..457612621...745457612938 B4: 1,7,8 # 18 pairs C4: 3,9,4,8 # reduction candidate for 3,9 C4: 3,9 => CTR * 742195386..8246571165...294....24.63234869157..6.3142989.457612621...745457612938 C4: 4,8 # 19 pairs * PAIR G5: 1,3 BLK 6 G4: 1,3,8 # reduction candidate for 1,3 G4: 1,3 => SOLVED * 743195286982346571165278493378524169214869357596731824839457612621983745457612938 G4: 8 => CTR * 74.1.5.86....46571165....9..1....86....86.157..6.31.2.8..457612621...745457612938 * PAIR G5: 1,3 ROW 5 B5: 1,3,9 # reduction candidate for 1,3 B5: 9 => CTR * 74.1.5.86....46571165....9..1.....6..9.864157576.31.2.8..457612621...745457612938 B5: 1,3 # 20 pairs * PAIR B7: 3,9 COL B B2: 3,9,8 # reduction candidate for 3,9 B2: 3,9 => CTR * 743195286298346571165..849338....16..1.86.357..6.318248..457612621...745457612938 B2: 8 => SOLVED * 743195286982346571165278493378524169214869357596731824839457612621983745457612938 B4: 3,9,1,7,8 # reduction candidate for 3,9 B4: 3,9 => CTR * 743195286.8.346571165..8493......16..1.86.357.765318248..457612621...745457612938 B4: 1,7,8 # 18 pairs B5: 3,9,1 # reduction candidate for 3,9 B5: 3,9 => CTR * 74.1.5.86.8..46571165...493518..4369..4869157976531824893457612621..3745457612938 B5: 1 => SOLVED * 743195286982346571165278493378524169214869357596731824839457612621983745457612938 * PAIR C7: 3,9 COL C C1: 3,9,2 # reduction candidate for 3,9 C1: 3,9 # 24 pairs C2: 3,9,2,8 # reduction candidate for 3,9 C2: 3,9 => CTR * 742195386.8..46571165....9...8..4.6...4869.57..6.318248..457612621...745457612938 C2: 2,8 # 19 pairs C4: 3,9,4,8 # reduction candidate for 3,9 C4: 3,9 => CTR * 742195386..8246571165...294....24.63234869157..6.3142989.457612621...745457612938 C4: 4,8 # 19 pairs C5: 3,9,2,4 # reduction candidate for 3,9 C5: 3,9 => CTR * 74.1.5.86....46571165....9...4..9.632..864157..6.31.298..457612621...745457612938 C5: 2,4 # 19 pairs * PAIR D8: 3,9 COL D D2: 3,9,2 # reduction candidate for 3,9 D2: 2 => CTR * 7421953863..24657116537829491..2..632..86.157..6.314298..457612621983745457612938 D2: 3,9 # 24 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190424-absurd-base-pr-000.dot * REASONING * DIS # D2: 2,9 => CTR => D2: 3 * DIS # C1: 2,9 => CTR => C1: 3 * DIS # G3: 2,3 => CTR => G3: 4 * PRF # G3: 4 => SOL * DIS # C1: 9 => CTR => C1: 2,3 * DIS # G3: 2 => CTR => G3: 3,4 * DIS # A4: 5,9 => CTR => A4: 3 * PRF # A4: 3 => SOL * DIS # D4: 2,7 => CTR => D4: 5 * PRF # D4: 5 => SOL * DIS # E3: 8 => CTR => E3: 2,7 * DIS # C4: 4,9 => CTR => C4: 3,8 * DIS # C5: 2,3 => CTR => C5: 4,9 * DIS # D4: 2 => CTR => D4: 5,7 * PRF # A4: 3,9 => SOL * DIS # A4: 5 => CTR => A4: 3,9 * DIS # B4: 3,9 => CTR => B4: 1,7,8 * DIS # C4: 3,9 => CTR => C4: 4,8 * PRF # G4: 1,3 => SOL * DIS # G4: 8 => CTR => G4: 1,3 * DIS # B5: 9 => CTR => B5: 1,3 * DIS # B2: 3,9 => CTR => B2: 8 * PRF # B2: 8 => SOL * DIS # B4: 3,9 => CTR => B4: 1,7,8 * DIS # B5: 3,9 => CTR => B5: 1 * PRF # B5: 1 => SOL * DIS # C2: 3,9 => CTR => C2: 2,8 * DIS # C4: 3,9 => CTR => C4: 4,8 * DIS # C5: 3,9 => CTR => C5: 2,4 * DIS # D2: 2 => CTR => D2: 3,9 * CNT 30 HDP CHAINS / 47 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B7,C7,D6,D8,E1,E4,E8,F3,F4,F5,F8,G1,G5,G6,I3,I4,I6) * 74.1.5.86....46571165....9........6....86..57..6.31.2.8..457612621...745457612938 * PAIR E1: 2,9 BLK 2 D2: 2,9,3 # reduction candidate for 2,9 D2: 2,9 => CTR * 74.1.5386....46571165...294.1....863...86.1575.6.314298..457612621...745457612938 * PAIR A6: 5,9 BLK 4 A4: 5,9,3 # reduction candidate for 5,9 A4: 5,9 => CTR * 74319528629.346571165..8.9........6.3.2864157..6.31.2.839457612621983745457612938 A4: 3 => SOLVED * 743195286982346571165278493378524169214869357596731824839457612621983745457612938 * DURATION: 0:00:03.785499 START: 05:35:12.984202 END: 05:35:16.769701 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190424-absurd-base-pr-001.dot * REASONING * DIS # D2: 2,9 => CTR => D2: 3 * DIS D2: 3 # A4: 5,9 => CTR => A4: 3 * PRF D2: 3 + A4: 3 => SOL * STA D2: 3 + A4: 3 * CNT 3 HDP CHAINS / 2 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019, 20190424, absurd
Solution
position: 743195286982346571165278493378524169214869357596731824839457612621983745457612938 solved
See section Pair Reduction for the HDP chains leading to this result.
Appendix: Full HDP Chains
A1. Pair Reduction Analysis
Full list of HDP chains traversed:
* DIS # D2: 2,9 => CTR => D2: 3 * INC # D2: 3 => UNS * DIS # C1: 2,9 => CTR => C1: 3 * INC # C1: 3 => UNS * DIS # G3: 2,3 => CTR => G3: 4 * PRF # G3: 4 => SOL * INC # C1: 2,3 => UNS * DIS # C1: 9 => CTR => C1: 2,3 * INC # G3: 3,4 => UNS * DIS # G3: 2 => CTR => G3: 3,4 * DIS # A4: 5,9 => CTR => A4: 3 * PRF # A4: 3 => SOL * DIS # D4: 2,7 => CTR => D4: 5 * PRF # D4: 5 => SOL * INC # E3: 2,7 => UNS * DIS # E3: 8 => CTR => E3: 2,7 * DIS # C4: 4,9 => CTR => C4: 3,8 * INC # C4: 3,8 => UNS * INC # C5: 4,9 => UNS * DIS # C5: 2,3 => CTR => C5: 4,9 * INC # D4: 5,7 => UNS * DIS # D4: 2 => CTR => D4: 5,7 * PRF # A4: 3,9 => SOL * DIS # A4: 5 => CTR => A4: 3,9 * DIS # B4: 3,9 => CTR => B4: 1,7,8 * INC # B4: 1,7,8 => UNS * DIS # C4: 3,9 => CTR => C4: 4,8 * INC # C4: 4,8 => UNS * PRF # G4: 1,3 => SOL * DIS # G4: 8 => CTR => G4: 1,3 * INC # B5: 1,3 => UNS * DIS # B5: 9 => CTR => B5: 1,3 * DIS # B2: 3,9 => CTR => B2: 8 * PRF # B2: 8 => SOL * DIS # B4: 3,9 => CTR => B4: 1,7,8 * INC # B4: 1,7,8 => UNS * DIS # B5: 3,9 => CTR => B5: 1 * PRF # B5: 1 => SOL * INC # C1: 3,9 => UNS * DIS # C2: 3,9 => CTR => C2: 2,8 * INC # C2: 2,8 => UNS * DIS # C4: 3,9 => CTR => C4: 4,8 * INC # C4: 4,8 => UNS * DIS # C5: 3,9 => CTR => C5: 2,4 * INC # C5: 2,4 => UNS * INC # D2: 3,9 => UNS * DIS # D2: 2 => CTR => D2: 3,9 * CNT 47 HDP CHAINS / 47 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # D2: 2,9 => CTR => D2: 3 * DIS D2: 3 # A4: 5,9 => CTR => A4: 3 * PRF D2: 3 + A4: 3 => SOL * STA D2: 3 + A4: 3 * CNT 3 HDP CHAINS / 2 HYP OPENED